How far can one move from a potential peak with small initial speed?
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- by Ângelo Barone Netto and Gaetano Zampieri PDF
- Proc. Amer. Math. Soc. 121 (1994), 711-713 Request permission
Abstract:
We consider a natural Lagrangian system and show that from a point ${q_0}$ in n-space, where the potential energy V has a (weak) maximum, one can go near the boundary of any compact ball where $V(q) \leq V({q_0})$ with (arbitrarily small) nonvanishing initial speeds. The result holds true for sets which are ${C^2}$-diffeomorphic to a compact ball. This property is found as a simple consequence of the Hopf-Rinow theorem and of a theorem of Gordon. As a corollary we deduce a well-known local result, namely, a ’converse’ of the Lagrange-Dirichlet theorem, thus obtained via geometric arguments.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 121 (1994), 711-713
- MSC: Primary 70H35; Secondary 58E99, 70K20
- DOI: https://doi.org/10.1090/S0002-9939-1994-1181156-X
- MathSciNet review: 1181156